Arthroplasty jig

ABSTRACT

A method and system for performing a total joint arthroplasty procedure on a patient&#39;s damaged bone region. A CT image or other suitable image is formed of the damaged bone surfaces, and location coordinate values (x n ,y n ,z n ) are determined for a selected sequence of bone surface locations using the CT image data. A mathematical model z=f(x,y) of a surface that accurately matches the bone surface coordinates at the selected bone spice locations, or matches surface normal vector components at selected bone surface locations, is determined. The model provides a production file from which a cutting jig and an implant device (optional), each patient-specific and having controllable alignment, are fabricated for the damaged bone by automated processing. At this point, the patient is cut open (once), the cutting jig and a cutting instrument are used to remove a selected portion of the bone and to provide an exposed planar surface, the implant device is optionally secured to and aligned with the remainder of the bone, and the patient&#39;s incision is promptly repaired.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation application of U.S.application Ser. No. 13/730,608 filed Dec. 28, 2012, which applicationis a continuation of Ser. No. 11/641,569 filed Dec. 18, 2006, whichapplication is a continuation of U.S. application Ser. No. 10/146,862filed May 15, 2002, abandoned. The above-referenced applications areincorporated by reference herein for all that they disclose or teach.

FIELD OF THE INVENTION

This invention relates to fabricating a value added medical device forpatient-specific, total joint arthroplasty (TJA) procedures. Morespecifically, the invention relates to a system for producing a valueadded medical device or instrument (collectively referred to as a“medical device” herein), based on computer tomography (CT) or otherimaging of a region of the body an adjacent to a selected joint.

BACKGROUND OF THE INVENTION

Surgeons are generally dexterous and highly trained to achieve astandardized level of surgical skill. However, surgeons havelimitations, including a lack of micron-level geometric accuracy. Forexample, a surgeon cannot place an instrument at an exact, numericallydefined location (within, say, 100 μm) relative to a patient's body partand then move the instrument through a defined trajectory. Many surgeonsare unable to exert a precise, predefined force in a selected direction.Furthermore, a surgeon may have small hand tremors that limit his/herability to operate on very small and delicate structures. Unfortunately,many of these limitations affect the outcome of certain surgicalprocedures, especially in cases where micron-level geometric accuracy isrequired. For example, the three-dimensional locations and directions ofbasic procedures used to modify a bone (including drilling, cutting, andreaming) determine the alignment and fit of the implant(s). Thesefactors directly influence these functional outcomes.

Recently, to assist surgeons in overcoming these limitations,computer-assisted surgery (CAS) utilizing robotic- or image-guidedtechnologies has been introduced into various medical fields. CAS, as acategorization or surgical technology, includes not only robotics butalso image-guided surgical devices, surgical navigation systems,pre-operative planners, and surgical simulators.

A primary goal of CAS technologies is to integrate pre-operativeplanting with intra-operative performance. One of the most importantsteps in integrating preoperative medical images directly into operatingroom procedures is registration of image and corresponding body part(s).Registration is a computational procedure that matches pre-operativeimages or planning information to the position of the patient on theoperating room table. Rigid pins or other fiducial markers were used inearly systems, such as in a robot-assisted system.

For robot-assisted total knee alignment (TKA) surgery, illustrated inFIG. 1, two spaced apart pins, 11A and 11B, are fixed to a target bone12 before CT images are formed of the damaged bone region 14. The phrase“CT imaging” or “CT scanning” will refer herein to any suitable two- orthree-dimensional imaging procedure, including computer tomography, andmagnetic resonance imaging. The pins, 11A and 11B, are used to allowalignment of a three-dimensional (3-D) reconstruction of the patientbone 12. The intraoperative locations of the pins are used to relate theposition of the patient's bone to a pre-operative plan, using a robotcontroller 14.

Based upon a converted CT scan image of the exposed bone(s) in thedamaged bone region, the location and angular orientation of the femoralmechanical axis (FMA), femoral anatomical axis (FAA) and tibialmechanical axis (TMA) are also determined, and a postoperative plan fororientation and movement of the milling machine 16 are determined in acoordinate system relative to the target bone 12, to mill the bone endaccording to a pre-programmed cutting file. After the registrationprocess i.e., matching the CT image bone model with the target boneusing the two pins, the robot assistant is activated, and the millingcutter attached to a robot arm mills the damaged bone region to createone (or preferably several) exposed planar surfaces (transverse,anterior, chamfer, etc.) to accept and mate with a femoral implant.

This method is accurate, to the extent that the ready-made implantdevice matches the patient's own bone surfaces, but requires at leasttwo surgical operations (including incisions or cutting for each): afirst operation for installation of a robotic calibration mechanism anda second operation for the final surgery to install the TKA deviceitself.

The second surgical operation is constrained by a tourniquet timelimitation, which places a practical limit on a maximum cumulative timean open wound can be exposed (usually 90-120 min. for TKA) withoutsevere danger of infection. This is another disadvantage ofrobot-assisted surgery, which requires use of a registration process andof a bone location fixation process, both time consuming. As compared torobot-assisted surgery, a conventional manual TKA procedure is usuallycompleted in no more than 30 minutes, despite a relatively highprobability of misalignment.

Shape-based registration, illustrated in FIG. 2, is an alternativemethod as shown in the previous art for TKA and THA that has beendeveloped recently and currently used in clinical trials. A patent'sdamaged bone 21D is exposed, in a first surgical operation. A locationcoordinate sensor 22 is placed in contact with the damaged bone surface21 at each of a selected sequence of spaced apart locations, and thecoordinates of each such surface point are received by a locationcoordinate processor 23 for subsequent processing. The processor 23provides an approximate equation for the surface of the damaged boneregion 21D. At least 15 surface coordinate triples are selected anddigitized on the actual bone surface, and the data are analyzed andprocessed to match, as closely as practicable, the CT scan image data,using interpolation, extrapolation and other suitable mathematicalapproximations. When a matching relation is found, optical or othersensors tack and guide a tracking device to provide a surgeon with thelocation and angular orientation information needed to identify asuitable implant device. For a TKA procedure, the image formation systemguides and locates the tracking device to provide location andorientation of transverse, anterior chamfer cuts to fit the femoralimplant.

Using the surface matching or registration technique illustrated in FIG.2, the shapes of a model of the bone surface 21, generated from a prooperative image, are matched to surface data points identified duringthe first incision or during surgery. Intra-operative surface datapoints can be specified by direct contact with percutaneous probes, fromwithin the surgical exposure using ultrasonic or direct-contact opticalprobes, or from fluoroscopic radiographic images. Location tracking is acritical step in CAS. Tracking devices are attached to a target bone andto my tools to be used during the operation, such as drills, reamers,guides, or screwdrivers. Many common tracking devices use opticalcameras and infrared light emitting diodes. These optical sensors areeasy to set up, very accurate, have fast sensing rates of up to 100measurements per second, and can tack multiple tools simultaneously. Adisadvantage of the devices illustrated in FIGS. 1 and 2 is that theyrequire additional surgical time, require a direct line of sight toperform the procedure, require special training of surgeon and staff,require maintenance and frequent calibration of the roboticmechanism(s), and can be very expensive, depending on the required levelof accuracy.

Other tracking technologies use acoustic or magnetic sensors that createan electromagnetic field around the surgical site that is altered asinstruments move within the field. Such devices do not require a directline of sight, but the devices may be less accurate, cannot be used withmetallic tools, and have difficulties tracking multiple toolssimultaneously. One major benefit of either of these tracking methods isa reduction in radiation, due to elimination of the need forintra-operative fluoroscopy or radiography to check component position.

The systems described in the preceding discussion often suffer from alack of readiness for the operating room and do not always addresspractical considerations. Many systems introduce additional capitalequipment, equipment maintenance and operative steps into the surgicalprocedures that prolong the surgery and require significant training.Further, most of the systems do not address the issues of sterility andsafety, and unwanted motion of the body part(s) to be operated upon.Most systems require input from the surgeon in order to specify data oralter program flow. Many systems rely on a non-sterile assistant toenter data, using a keyboard, mouse or pen, but this is inefficient andrisks miscommunication. A sterilized or draped input device, introducedinto the surgical operating theater, may be difficult to use, may bedistracting for the surgeon, requires the splitting of the surgeon'sattention between the display screen in one location and the surgicaltool in another, and requires removal of the tool from the surgical sitefor use elsewhere as an input device.

What is needed is a system that requires only one surgical procedure(defined as requiring at least one incision or cutting operation),employs a pre-operative scanning procedure that provides micron levelaccuracy, is flexible enough to account for certain tolerances relativeto an idealized fit, and provides a fabricated, patient-specific cuttingjig and a patient-specific (optional) implant device whose componentscan be aligned and altered according to the body part(s) involved.

SUMMARY OF THE INVENTION

The needs discussed in the preceding paragraph are met by the invention,which uses pre-operative scanning and construction of a geometric modelof the target body part surface, pre-operative fabrication of apatient-specific cutting jig and a patient-specific (optional) implantdevice, which may have one or more than one component, monitoring and acorrection of the jig and/or implant device, vis-a-vis the target bodypart, and relies on a single surgical procedure to remove a selectedpart of a damaged bone and to implant and initially test an implantdevice (optional) in vivo.

One feature of the invention is use of an image-based surgical system intotal joint arthroplasty, such as total hip arthroplasty (THA), totalknee arthroplasty (TKA), total elbow arthroplasty (TEA), spinal surgery,etc. The system software receives or provides geometrical information onthe damaged bone, captured in CT or another suitable imaging format, andconverts his information into a three-dimensional (3D) model of the bonesurfaces during the computer-aided pre-operative planning. The converted3-D model includes the information on corresponding bone dimensionsalong with the uncertainties associated with CT scanning and conversionerrors. The system displays all the pertinent information on the damagedbones on the screen. The system provides a surgeon with improvedvisualization of the relationship between the damaged bone and thecutting jig or implant device, including but not limited to accuratealignment of the device, by accurately superimposing representations ofa cutting jig and/or an implant device being used in the surgical fieldover the images of the bone.

Another feature of the invention is that, once the planning is complete,the system software prepares and provides a computer file to directrapid production machines, such as a computer numerical control (CNC)machine, a stereo-lithograph (SLA) machine, etc., to fabricate a cuttingjig and/or an implant device (optional), which may be disposable(replaceable) or non-disposable (recyclable). The value added cuttingjig and/or implant device is made of any bio-compatible material andworks with a manual and/or automated instrument to transfer jointplanning information between a computer-aided pre-operative planningphase and the actual surgical procedure. During surgery, the cutting jigis employed to guide critical cuts and shaping of the bone, such asdrilling, reaming, sawing, etc. The cutting jig and/or implant device(optional) includes a surface profile that matches the bone surfaces invivo.

With reference to the cutting jig surface profile, guiding holes fordrilling and inspection, a slot feature for a sawing process, andbushing features for reaming and drilling are fabricated. Alternatively,the surface profile can be created with reference to guiding holes,slots and bushings.

A related feature of the invention is that the system software performsvirtual surface mapping techniques with respect to the 3D model based onCT scan images, including point-to-point mapping, surface normal vectormapping, and surface-to-surface mapping techniques. Depending on theapplication, one or a combination of mapping techniques can be employed.

Another feature of invention is that the system software includestransferring of all pre-operative planning data and related computerfiles to a production floor model through a selected communicationsystem (e-mail, file transfer protocol, web-browser, LAN, fiber opticcable, wireless, etc. and/or manual transfer).

Another feature of the invention is that, upon receiving the data from aremote planning station, the system software automatically executes andprovides information pertinent to the rapid production and inspectionprocesses. A quality control procedure includes monitoring andverification of 1) the surface profile of a cutting jig and of an(optional) surgical implant device compared to the 3-D profile of thebone virtual surface from the CT image and 2) Station and angularpositioning of the fabricated features such as drilling holes, slots andbushings. Later, the jig and the (optional) implant device are cleaned,sterilized (optional), packaged and delivered to the surgical operatingtheater.

These features and advantages of the present invention are embodied inan improved system for assisting a surgeon in using a surgical tool toprovide accurate cutting, implant positioning and alignment with respectto one or more body parts. The system uses a computer-aided calibrationprocess involving a surface matching of the cutting jig and/or implantdevice to the bone surface(s). Because the cutting jig and/or implantdevice is fabricated using CT scan image data, there is no need for useof a registration process, expensive tracking systems or robotic systemsin an operating room, or for use of two or more surgical procedures. Theinvention is designed rework in conjunction with any manual standard TJAinstrumentation, and thus minimizes additional expenditures for capitalequipment purchases. Furthermore, there is no increase in surgical time,and the cutting jig and/or implant device can provide a reduction insurgical time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates robot-assisted total knee arthroplasty (TKA).

FIG. 2 illustrates shape-based registration in TKA.

FIG. 3A illustrates a damaged region of a target bone undergoing CTscan.

FIG. 3B illustrates the target bone as shown in FIG. 3A with a jighaving a transversely oriented slot or aperture to accept a cuttinginstrument, such as a saw blade.

FIG. 3C illustrates the target bone as shown in FIG. 3A with the damagedregion having been removed.

FIG. 3D illustrates a fabricated implant device.

FIGS. 4A/4B are a flow chart of a procedure for practicing theinvention.

FIG. 5 illustrates a non-invasive bone positioning device used inpre-operative planning according to the invention.

FIG. 6 illustrates three axes of interest on a femur and a tibia.

FIG. 7 illustrates pre-operative planning and measuring according to theinvention.

FIGS. 8A/8B/8C are schematic views of a surgical implant device for TKA,prepared according to the invention.

FIG. 9 is a schematic view of mating of a component of the implantdevice and a body part (femur) of the patient.

FIGS. 10A, 10B, 11 and 12 illustrate a procedure for estimating a localshape function for point-to-point matching on a surface.

FIG. 13 illustrates a procedure for estimating a local surface forsurface normal vector matching.

DETAILED DESCRIPTION OF THE INVENTION

1) System Architecture

In a preferred embodiment, the invention provides accurate positioningand alignment of an orthopedic implant without a significant increase insurgical time or capital equipment cost. Also, during the actualsurgery, the system does not require use of registration, image matchingor location tracking, which distinguishes the invention from otherimage-based systems.

FIGS. 3A, 3B, 3C and 3D illustrate some features of the invention. Adamaged region 31D of a target bone 31 undergoes CT scan in FIG. 3A.Pre-operative planning is performed, using a computer and a CT imagescanner 32, to construct a model of bone suffices adjacent to thedamaged region 31D, with an associated inaccuracy of no more than 90 μm.Based on the accumulated planning data, a production file is created toreceive the CT image data and to fabricate a jig or cutting block and,optionally, an implant device. The production file and the planninginformation are sent to the production floor for fabrication of apatient-specific jig and a corresponding implant device patient-specificor off-the-shelf.

In FIG. 3B, a jig 33 is fabricated to seat against the femur (or againstthe tibia, for tibia processing) and has a transversely oriented slot oraperture 33S that accepts and provides a guide for a cutting instrument34, such as a reciprocating saw blade. After incision in the patient'sbody, the cutting instrument 34 would be placed in and aligned with theslot 33S so that, when the cutting instrument is activated and the femur(or tibia) is exposed, a distal end portion of the femur (or proximalend portion of the tibia) can be removed to provide a planar exposedsurface 35, as illustrated in FIG. 3C.

Note that no incision into or cutting of the patient's body has yetoccurred; the jig 33 and slot 33S are designed and fabricated usingprimarily the information obtained from the CT image scan. An implantdevice 36, illustrated in FIG. 3D and having a planar surface, isoptionally fabricated from the CT scan information, without incisioninto or cutting of the patient's body.

The fabricated jig 33 and optional implant device 36 are delivered to asurgical operating theater, and the patient's body is cut open to exposeat least the distal end of the femur 31 and the proximal end of thetibia in the damaged bone region 31D. The jig 33 and slot 33S arepositioned, and a member of the surgical team removes a portion of thedistal end of the femur 31 (and, similarly, removes a portion of theproximal end of the tibia) to provide an exposed and aligned planarsurface 35 (and, similarly, to provide an exposed and aligned planarsurface of the tibia). The femur jig 33 is then removed, and acorresponding planar surface of the femur implant device 36 isoptionally attached to the exposed planar surface of the femur distal.This attachment may be done using one, two, three or more attachmentmechanisms, such as bolts, screws or nails, that attach the femurimplant device 36 to the remainder of the distal end of the femur, atthe femur planar surface 35. In a similar manner, a tibia implant deviceis attached to the remainder of the proximal end of the tibia at thetibia planar surface.

During the surgery, the custom mating between the jig 33 and theremainder of the target bone (femur and/or tibia) at the exposed planarsurface ensures a precise fit (location and alignment, drilling holesand a slot 33S) for surgeons in performing the joint repair/replacementprocess with any manual standard instrumentation.

FIGS. 4A/4B are a flow chart for practicing the invention. In step 41, adamaged region of a bone, or of one or more adjacent bones, isoptionally identified. In step 42, a CT image is formed of the damagedbone region and, preferably, of all portions of each bone involved inthe damaged region (e.g., proximal end of the femur and/or distal end ofthe tibia). For example, if a femur-tibia connection at a knee isdamaged, a CT image of the full length of the femur and of the fulllength of the tibia are preferably formed, including the ends of thesebones that are not involved in the damaged bone region. In step 43,location coordinate values of each of a sequence of spaced apart surfacepoints on each bone in the damaged bone region are determined from theCT image. Optionally, these location coordinates are referenced to anabsolute coordinate system associated with the damaged bone region.

In step 44, a model of a bone surface in the damaged bone region isestimated or computed, using a mathematical method described herein oranother appropriate method. Optionally, the surface points are used tosubdivide the bone surface in the damaged bone region into a sequence ofpolygons P, preferably triangles and/or quadrilaterals, as part of thesurface modeling process. At least three approaches are available here.

In a first approach, a mathematical model of the surface is developedion that matches, as closely as possible, the coordinate values(x_(n),y_(n),z_(n)) of each of the sequence of surface location pointsprovided by the CT image. Here, the bone surface may be modeled withineach of the sequence of polygons P, and the sequence of approximationscan be treated collectively for the bone surface as a whole; or the bonesurface may be modeled in the large by a single polynomial,trigonometric series or other function set in appropriate locationcoordinates, such as Cartesian coordinates (x,y,z).

In a second approach, a surface normal at a selected point within eachof the sequence of polygons P is measured or otherwise provided, usingthe CT image information, and a surface portion within that polygon isdetermined for which the surface normal matches, as closely as possible,the CT image-provided surface normal at the selected point. In a thirdapproach, use of surface point locations and surface normal vectors arecombined.

In step 45, the mathematical model determined for the bone surface inthe damaged bone region is used, as part of a production file, togenerate automated instructions for fabricating a cutting jig and animplant device (optional) for each of the femur and the tibia. In step46, the cutting jig and the implant device (optional) are fabricated,using the production file cutting jig preferably includes a planarsurface to allow the implant device to mate with and align with thebone.

In step 47, one or more incisions is made on the patient's body toexpose the damaged bone region and to allow access to the damaged boneregion. The cutting jig is used to remove a selected end portion of thebone and to provide an exposed planar surface of the bone remainder.

In step 48, a selected portion of the damaged bone is removed, using thecutting jig, to provide a planar surface against which an implant devicewill be (optionally) fitted.

In step 49, the implant device is optionally fitted to, and securedagainst, the planar surface of the bone remainder, and alignment of theimplant device with one or more bone axes and implant device attachmentis implemented. In step 50, the surgical incisions in the patient's bodyare repaired; the patient's body is “sewn up” (once). Only one surgicalprocedure, with its concomitant incisions and cutting, is required here,and this surgical procedure requires an estimated 20-25 minutes tocomplete, including bone end remainder and implant device alignment andattachment.

The following is a more detailed discussion of practice of the inventionfor TJA, where the damaged bone region is a patent's knee.

Stage I:

A non-invasive bone fixturing device 51 is provided (not requiringcutting or piercing of the skin), including a system of rigid bars, 52Aand 52B, strapped to and immobilizing the patient's femur 53 and tibia54 by a plurality of elastic steps, 55A and 55B, as shown in FIG. 5.Optionally, the bone fixturing device 51 is also used as a referenceframe. The damaged knee (or other joint) of the patient is CT scannedand processed into a computer file, using a selected reference frame.With the exception of severely abnormal or fractured knee joints, the CTscan concentrates on pertinent areas, in and around the damaged boneregion, that will assist in determining the femoral mechanical axis(FMA), femoral mechanical center (FMC), femoral anatomical axis (FAA)and tibial mechanical axis (TMA), as shown in FIGS. 5 and 6. The CTimage data, including data conversion into a 3-D geometric format, arereceived by a computer, and the system automatically performs thefollowing: (1) A 3D conversion algorithm is utilized to provide 3Dgraphical representation of the knee components, where the algorithmprovides optimal graphical representation for the knee implants'planning process as well as downstream production applications; and (2)The system software analyzes bone motion detection and re-configurationalgorithms. If bone motion is detected, the system analyzes andre-configures the bones (here, femur 53 and tibia 54) with respect tothe bone positions. If too much movement is detected, the systemrecommends re-scanning the knee to provide a new image.

Stage II:

The 2D and 3D models of the knee from Stage I are viewable on thepreoperative plug system PC display as well as a library LINK of thefemoral and tibial knee implant components. The library includes 3Dmodels of various size implants and other ancillary parts. The names ofthe implant manufacturers and manufacturer's surgical criteria andoptimum alignment conditions for implant installation will also beavailable. As an example, using the system to determine the FMA, thesurgeon may execute the following sequence: (1) select the center of thefemoral head with an icon; (2) select the center of the knee (other endof the femur) with another icon; and (3) connect the two icons with astraight line. This defines an FMA, one of the axes, as illustrated inFIGS. 5, 6 and 7. If the surgeon has a preferred way of determining theFMA, the surgeon has the flexibility to use any desired graphicalmethod. For ascertaining the FAA and the TMA, also shown in FIG. 7,similar techniques are implemented.

Similar to commercially available graphic software, the preoperativeplanning system includes capabilities for enlargement, shrinking,panning, zooming, rotating, etc. As shown in FIG. 7, a plane 72,perpendicular to FMA, represents a transverse cut of the distal femur 53(and of the proximal tibia 54); this information is used to create aslot for transverse cutting during the actual surgery.

The system allows a surgeon to perform the following: (1) check theresults of the pre-operative planning to avoid or minimize theconsequences of mistakes; and (2) simulate and recommend other availableorthopedic theories, techniques and case studies, i.e., for bowed legsand fractured knees, which will be based on recent literature, surveysand widely accepted knee kinematics and alignment theories. Thisparticular portion of the system is optional; the surgeon makes thefinal decisions in implant planning.

Stage III:

The system generates a production file, including a machining orfabrication file, based upon information of the planned position andalignment of the femoral and tibial components from the previous stage.This file is used to control a production machine that fabricates thepatient-specific jigs for both femoral and tibial aspects of the knee.These unique jigs, an example of which is shown in FIGS. 8A/B/C,implement transfer and use of information between preoperative planningand surgery and allow a member of the surgery team to provide a clean,precise slice and an exposed planar surface of the remainder of thebone. The production file creates one or more selected internal (mating)surfaces of the exterior surface profile for the damaged knee surfacegeometry, for accurate patient-specific mating between the jig and theremainder of the patient's distal femur. In addition, the productionfile creates a transversely oriented slot and cutting instrument guidefor a transverse cutting process. These features are optionally createdwith respect to the inter-condylar aperture (FAA) as a reference point.Accurate mating between the jig and the distal end of the femur ensuresthe accurate translation and angular position of the slot as planned inSTAGE II. This provides the surgeon with access to a transverse cut onthe distal femur, which establishes the correct alignments and providesreference planes for assembling manual instrumentation for the rest ofthe cuts required for knee implant installation.

FIGS. 8A and 8B are perspective views of a cutting jig, 81 and 86,fabricated according to the invention. The model of the damaged boneregion is used to define a selected region 82 to be removed from a block83 of hardened material (preferably a biocompatible plastic) that is afirst component 81 of the cutting jig. The region 82 is selected so thatthe damaged bone region will fit snugly into the hollowed-out region inthe block 83. First and second lateral projections, 84A and 84B, areprovided on the block 83, with each projection having an aperture thatis approximately perpendicular to an initial surface 83S of the block83. A second component 86 of the cutting jig includes third and fourthprojections, 87A and 87B, that mate with the respective first and secondprojections, 84A and 84B, of the first component 81. Apertures in thethird and fourth projections, 87A and 87B, mate with and are alignedwith the apertures in the first and second projections, 84A and 84B,respectively. When the first jig component 81 is mated with the secondjig component 86, a small, transversely oriented gap 88 is definedbetween the first and second jig components, into which a cuttinginstrument can be inserted to cut off and remove a damaged region of thebone, as illustrated in FIG. 8C. After a transverse cut is made, usingthe jig 81/86, a first aperture is formed in the remainder of the bone,along the bone longitudinal axis, and one or more additional aperturesare formed, parallel to and spaced apart from the first aperture. Theseapertures are used to align an implant device with the bone remainder.

The system automatically determines the correct size of the jigs for thedistal end of the femur and the proximal end of the tibia (53 and 54 inFIG. 5). The system includes an algorithm for determining optimum matingconditions through volume and tolerance/interference checks between thepatient knee and the jigs. FIG. 9 illustrates how the virtual mating ofthe patient-specific jig components, 81 and 86, to the distal femur 53are displayed on a PC screen. The system includes an algorithm thatperforms the following functions: (1) generation of efficient productionprocesses; and (2) determination of production parameter conditions. Inthis stage, no surgeon or user intervention occurs, and the productionfile along with CT image file is transferred from the hospital planningstation to a rapid production floor through a secure inter-netconnection or other methods.

Stage IV:

The patient-specific jigs (optionally disposable) are fabricated withrapid production machines. The fabricated features are inspected througha quality control procedure. During the production process, reportingstatus and error conditions are critical. In order to achieve highquality surface mating, the accommodation of control modules thatactively monitor and adjust the machining process should be considered.The system automatically executes and provides information pertinent tothe production and inspection processes. The quality procedure involvesmonitoring and verification of (1) the profile surface of the jigscompared to the profile of the knee surface determined from the CT imageand (2) translation and angular positioning of the machined featuressuch as transverse and tibial cutting slots. Finally, the jigs arecleaned, sterilized (optional), labeled, packaged and delivered to thehospital. As yet, no cutting of the patient's body bas occurred.

Modeling of a Bone Surface

Other inventions require so called shape-based registration that theshapes of the bone surface model generated from a pre-operative imageare matched to surface data points collected during a first phase ofsurgery. This surface matching method requires finding a mappingrelation (transformation matrix) between bone surface data points andthe bone surface model. Therefore, the accuracy of registration processdepends on the number of points and distance between each point. Oncethe mapping relation is found, the pre-operative plan can be performedbased on the mapping relation during the surgery. The mapping relationbetween surface data points and the bone surface model from apreoperative image can provide surgeons with the pre-operative imagebased planning information needed for a successful surgery. A key to thesuccess of this method is determination of an accurate bone surfacerepresentation of a preoperative image. The more accurate the bonesurface model is, the more precise the position and alignment of theimplant device.

This invention differs from other approaches in not requiring use of aregistration process during actual surgery. The invention relies upon avirtual registration process for a bone surface mathematical modelgenerated from a pre-operative, CT scanned image. In order to achievethis goal, the invention includes the interpolated deterministic datapoints as well as uncertainty associated with each point. Thisuncertainly information is critical for the production of surgicaldevice (hardware) and surgical error analysis prior to surgery.

Several approaches can be used for virtual registration.

(1) Point-to-point mapping on the bone surface model. Virtual datapoints on the 3D CT bone surface are selected to accurately describe thedistal femur and the proximal tibia in the damaged bone region. Based onthe selected data points, virtual pins are introduced at selectedsurface points with corresponding coordinate values, such as (x,y,z),that are to be used to map the bone surface at these locations. Thedirections of all virtual pins are straight and may be parallel to, ortransverse to, the femoral anatomical axis (FAA). No particular pindirection is required. A pin can point at each selected surface point inany direction, for example in a direction of a surface normal at thatsurface point. Once the pre-operative planning is completed, an implantdevice can be fabricated using available manufacturing techniques. Thesurgical hardware can be disposable or re-usable. During surgery, theimplant device with pre-operative planning information, such as slotposition and drilling hole locations, is placed on the distal femur.Custom mating between the surgical device and the distal (or proximal)bone surface ensures accurate mapping relation between the actual bonesurface and the bone surface model. The more data points are selected,the more accurate surgical result is obtained.

(2) Surface normal vector mapping on the bone surface model. Sufficientvirtual data points on the 3D CT image bone surface are selected todescribe the geometry of the distal femur and the proximal tibia. Basedon the selected data points, virtual pins and pin directions areintroduced at the selected data points, with the direction of eachvirtual pin being normal to the surface at each selected point. Thevirtual pin directions are arbitrary, but a pin direction normal to thelocal surface is preferred. Once this pre-operative planning iscompleted, surgical device can be made using any available manufacturingtechniques. The surgical hardware, including jig, can be disposable ofre-usable. During surgery, the implant device (patient-specific oroff-the-shelf), including pre-operative planning information, such asslot position, drilling hole locations is fabricated and placed on thedistal femur. Custom mating between the implant device and the distalbone surface ensures accurate mapping relation between the actual bonesurface and the bone surface model. A sufficient number of source pointlocations and corresponding normal vector component values aredetermined (preferably five or more) to provide an accurate model of thebone surface.

(3) Local surface mapping on the bone surface model. Several localmating virtual areas on the 3D CT image bone surface are selected todescribe a geometry of the distal femur and proximal tibia. The localsurface-to-surface mapping is equivalent to case (2), surface normalvector mapping, but uses a significantly larger number of data points.Once this pre-operative planning is completed, surgical device can bemade using any available manufacturing techniques. The surgical hardwarecan be disposable or re-usable. During surgery, the implant device withpre-operative planning information, such as slot position, drilling holelocations is placed on the distal femur. Custom mating between theimplant device and the distal bone surface ensures accurate mappingrelation between the actual bone surface and the bone surface model. Useof a local area surface mapping approach can significantly increase theaccuracy and reliability of the surgery.

(4) Global surface mapping on the bone surface model. One global matingvirtual area on the 3D CT image bone surface is determined to describethe geometry of the distal femur and proximal tibia. A global asurface-to-surface mapping is employed, and this approach is equivalentto case (3), the local surface mapping on the bone surface model, withthe increased surface contact areas. Once this pre-operative planning iscompleted, surgical device can be made using any available manufacturingtechniques. The surgical hardware can be disposable or re-usable. Duringsurgery, the implant device with pre-operative planning information,such as slot position, drilling hole locations is placed on the distalfemur. Custom mating between the implant device and the distal bonesurface ensures accurate mapping relation between the actual bonesurface and the bone surface model.

Precise pre-operative planning is essential for a successful TJA.Several techniques of CT-based pre-operative planning have beendeveloped. The system allows the surgeon to develop a plan of componentplacement in TJA. Surgeons can check the plan that they have made byreferring to the geometric relationship with respect to the implant.

A repaired knee joint, or other joint, may fail prematurely, for any ofseveral reasons. Instability of the implant device, due to kinematicmisalignment, may cause such failure and may require performance of arevision TKA. This is a delicate surgical procedure in which additionalbone loss, due to realignment, must be minimized. A revision TKA beginswith removal of the original implant device and of any bone cementremaining between the implant device and the exposed bone surface.During pre-operative planning, a bone surface image can be formed andpreserved, not including the bone cement and implant device surfaces.Based on his (preserved) image data, another patient-specific jig isfabricated with its own (corrected) cutting slot, using the techniquesdiscussed for primary or original TKA. Because all bone surfaces arealready shaped due to the earlier primary TKA procedure, use of asurface-to-surface mapping would be appropriate here.

Mathematical Details of Bone Surface Matching.

FIGS. 10A and 10B are views of a slice of an end of a bone 151, such asa femur or a tibia, that is analyzed using a CT scan to provide anestimate of a surface shape function z=f_(s)(x,y) that accuratelydescribes an end portion of the bone. An (x,y,z) Cartesian coordinatesystem is shown imposed on the bone 151, with the z-axis orientedapproximately parallel to a longitudinal axis LL of the bone, and theslice optionally corresponds to a plane a′x+b′y=constant; forconvenience in notation, it may be assumed here that a=0. In FIG. 10A, asequence of spaced apart points with coordinates (x_(n),y_(n),z_(n))(n=1, 2, . . . , 27) are shown for the slice.

In a first approximation, first and second sequences of incrementalratios or derivative approximations(Δx/Δz)_(n)=(x _(n+1) −x _(n))/(z _(n+1) −z _(n)),  (1)(Δy/Δz)_(n)=(y _(n+1) −y _(n))/(z _(n+1) −z _(n)),  (2)

are computed, using a linear approximation ratio for each of thederivatives. The first sequence of derivatives {(Δx/Δz)_(n)}_(n) is thensubdivided into a group of one or more mutually exclusive sub-sequences{(Δx/Δz)_(nk)}_(k) (k=1, . . . , K), with each sub-sequence having aconsecutive subset of the ratios (Δx/Δz)_(n) with monotonicallyincreasing, or monotonically decreasing, numerical values for thederivatives. In a similar manner, the second sequence of derivatives{(Δy/Δz)_(m)}_(m) is then sub-divided into a group of one or moremutually exclusive sub-sequences {(Δy/Δz)_(mj)}_(j) (j=1, . . . , J),with each sub-sequence having a consecutive subset of the ratios(Δy/Δz)_(m) with monotonically increasing, or monotonically decreasing,numerical values for the derivatives. Within each of the regions wherethe derivatives are monotonic, a simplified approximation to the localsurface can be used.

The preceding equations are used to define regions of mating along thefemoral anatomical axis. A change in slope from monotonic increase todecrease, or from monotonic decrease to increase, indicates that matingis no longer possible with respect to the FAA.

(1) Point-to-point bone surface mapping. Consider a quadrilateralQ(1,2,3,4), having a non-zero enclosed area and defined by four adjacentbut distinct points, having coordinates (x_(n),y_(n),z_(n)) (n=1, 2, 3,4), as illustrated in FIG. 11, that are determined, using a CT scan, tolie on a surface BS of the bone 151 in FIGS. 10A and 10B. One goal is todetermine a shape function z=f_(s)(x,y) that is differentiable within apolygonal region and that satisfies z_(n)=f_(s)(x_(n),y_(n)) for n=1, 2,3, 4. Consider first a situation in which no two or more x-coordinatevalues x_(n) are equal and no two or more y-coordinate values y_(n) areequal, referred to as a (4,4) situation, indicating that four distinctx-coordinates values and four distinct y-coordinate values are needed todefine the quadrilateral Q(1,2,3,4). In this (4,4) situation, onesuitable shape function for a quadrilateral grid is

$\begin{matrix}\begin{matrix}{z = {f_{s}\left( {x,{y;4;4;{qu}}} \right)}} \\{= {{z_{1}\left( {x - x_{2}} \right)}\left( {x - x_{3}} \right)\left( {x - x_{4}} \right)\left( {y - y_{2}} \right)\left( {y - y_{3}} \right){\left( {y - y_{4}} \right)/}}} \\{\left( {{d_{x}\left( {{1;2},3,4} \right)} \cdot {d_{y}\left( {{1;2},3,4} \right)}} \right) +} \\{{z_{2}\left( {x - x_{1}} \right)}\left( {x - x_{3}} \right)\left( {x - x_{4}} \right)\left( {y - y_{1}} \right)\left( {y - y_{3}} \right){\left( {y - y_{4}} \right)/}} \\{\left( {{d_{x}\left( {{2;1},3} \right)} \cdot {d_{y}\left( {{2;1},3,4} \right)}} \right) +} \\{{z_{3}\left( {x - x_{1}} \right)}\left( {x - x_{2}} \right)\left( {x - x_{4}} \right)\left( {y - y_{1}} \right)\left( {y - y_{2}} \right){\left( {y - y_{4}} \right)/}} \\{\left( {{d_{x}\left( {{3;1},2,4} \right)} \cdot {d_{y}\left( {{3;1},2,4} \right)}} \right) +} \\{{z_{4}\left( {x - x_{1}} \right)}\left( {x - x_{2}} \right)\left( {x - x_{3}} \right)\left( {y - y_{1}} \right)\left( {y - y_{2}} \right){\left( {y - y_{3}} \right)/}} \\{\left( {{d_{x}\left( {{4;1},2,3} \right)} \cdot {d_{y}\left( {{4;1},2,3} \right)}} \right),}\end{matrix} & (3) \\{{{d_{x}\left( {{a;b},c,d} \right)} = {\left( {x_{a} - x_{b}} \right) \cdot \left( {x_{a} - x_{c}} \right) \cdot \left( {x_{a} - x_{d}} \right)}},} & (4) \\{{d_{y}\left( {{a;b},c,d} \right)} = {\left( {y_{a} - y_{b}} \right) \cdot \left( {y_{a} - y_{c}} \right) \cdot {\left( {y_{a} - y_{d}} \right).}}} & (5)\end{matrix}$

At each of the four locations (x_(n),y_(n),z_(n)), three of the fourterms in the expression for z=f_(s)(x,y;4;4;qu) vanish, andf_(s)(x_(n),y_(n);4;4;qu)=z_(n).

In a (3,4) situation, only three of the four x-coordinate values aredifferent (e.g., x3≠x1=x2≠x4≠x3), but all four of the y-coordinatevalues are different from each other. In this (3,4) situation, the shapefunction is defined to be:

$\begin{matrix}\begin{matrix}{z = {f_{s}\left( {x,{y;3;4;{qu}}} \right)}} \\{= {{z_{1}\left( {x - x_{3}} \right)}\left( {x - x_{4}} \right)\left( {y - y_{2}} \right)\left( {y - y_{3}} \right){\left( {y - y_{4}} \right)/}}} \\{\left( {{d_{x}\left( {{1;3},4} \right)} \cdot \;{d_{y}\left( {{1;2},3,4} \right)}} \right) +} \\{{z_{2}\left( {x - x_{3}} \right)}\left( {x - x_{4}} \right)\left( {y - y_{1}} \right)\left( {y - y_{3}} \right){\left( {y - y_{4}} \right)/}} \\{\left( {{d_{x}\left( {{2;3},4} \right)} \cdot \;{d_{y}\left( {{2;1},3,4} \right)}} \right) +} \\{{z_{3}\left( {x - x_{1}} \right)}\left( {x - x_{4}} \right)\left( {y - y_{1}} \right)\left( {y - y_{2}} \right){\left( {y - y_{4}} \right)/}} \\{\left( {{d_{x}\left( {{3;1},4} \right)} \cdot \;{d_{y}\left( {{3;1},2,4} \right)}} \right) +} \\{{z_{4}\left( {x - x_{1}} \right)}\left( {x - x_{3}} \right)\left( {y - y_{1}} \right)\left( {y - y_{2}} \right){\left( {y - y_{3}} \right)/}} \\{\left( {{d_{x}\left( {{4;1},3} \right)} \cdot \;{d_{y}\left( {{4;1},2,3} \right)}} \right),}\end{matrix} & (6) \\{{{d_{x}\left( {{a;b},c} \right)} = {\left( {x_{a} - x_{b}} \right) \cdot \left( {x_{a} - x_{c}} \right)}},} & (7) \\{{d_{y}\left( {{a;b},c} \right)} = {\left( {y_{a} - y_{b}} \right) \cdot {\left( {y_{a} - y_{c}} \right).}}} & (8)\end{matrix}$

For the (4,3) situation, with four distinct x-coordinates values andonly three distinct y-coordinate values, the shape functionz=f_(s)(x,y;4;3;qu) is defined analogous to the shape functionz=f_(s)(x,y;3;4;qu) in Eq. (6).

In a (2,4) situation, only two of the four x-coordinate values aredifferent (e.g., x1=x2≠x3=x4), but all four of the y-coordinate valuesare different from each other. In this (2,4) situation, the shapefunction is defined to be:

$\begin{matrix}\begin{matrix}{z = {f_{s}\left( {x,{y;2;4;{qu}}} \right)}} \\{= {{{z_{1}\left( {x - x_{3}} \right)}\left( {y - y_{2}} \right)\left( {y - y_{3}} \right){\left( {y - y_{4}} \right)/\left( {{d_{x}\left( {1;3} \right)} \cdot {d_{y}\left( {{1;2}{,3,4}} \right)}} \right)}} +}} \\{{{z_{2}\left( {x - x_{3}} \right)}\left( {y - y_{1}} \right)\left( {y - y_{3}} \right){\left( {y - y_{4}} \right)/\left( {{d_{x}\left( {2;3} \right)} \cdot {d_{y}\left( {{2;{1\;}},3,4} \right)}} \right)}} +} \\{{{z_{3}\left( {x - x_{1}} \right)}\left( {y - y_{1}} \right)\left( {y - y_{2}} \right){\left( {y - y_{4}} \right)/\left( {{d_{x}\left( {3;1} \right)} \cdot {d_{y}\left( {{3;1},2,4} \right)}} \right)}} +} \\{{{z_{4}\left( {x - x_{1}} \right)}\left( {y - y_{1}} \right)\left( {y - y_{2}} \right){\left( {y - y_{3}} \right)/\left( {{d_{x}\left( {4;1} \right)} \cdot {d_{y}\left( {{4;1},2,3} \right)}} \right)}},}\end{matrix} & (9) \\{{{d_{x}\left( {a;b} \right)} = \left( {x_{a} - x_{b}} \right)},} & (10) \\{{d_{y}\left( {a;b} \right)} = {\left( {y_{a} - y_{b}} \right).}} & (11)\end{matrix}$

For the (4,2) situation, with four distinct x-coordinates values andonly two distinct y-coordinate values, the shape functionz=f_(s)(x,y;4;2;qu) is defined analogous to the shape functionz=f_(s)(x,y;2;4;qu) in Eq. (9).

In a (3,3) situation, only three of the x-coordinate values aredifferent (e.g., x3≠x1=x2≠x4≠x3), and only three of the y-coordinatevalues are different (e.g., y4≠y1≠y2=y3≠y4). In this (3,3) situation,the shape function is defined to be:

$\begin{matrix}\begin{matrix}{z = {f_{s}\left( {x,{y;3;3;{qu}}} \right)}} \\{= {{{z_{1}\left( {x - x_{3}} \right)}\left( {x - x_{4}} \right)\left( {y - y_{2}} \right){\left( {y - y_{4}} \right)/\left( {{d_{x}\left( {{1;3},4} \right)} \cdot {d_{y}\left( {{1;2},4} \right)}} \right)}} +}} \\{{{z_{2}\left( {x - x_{3}} \right)}\left( {x - x_{4}} \right)\left( {y - y_{1}} \right){\left( {y - y_{4}} \right)/\left( {{d_{x}\left( {{2;3},4} \right)} \cdot {d_{y}\left( {{2;1},4} \right)}} \right)}} +} \\{{{z_{3}\left( {x - x_{1}} \right)}\left( {x - x_{4}} \right)\left( {y - y_{1}} \right){\left( {y - y_{4}} \right)/\left( {{d_{x}\left( {{3;1},4} \right)} \cdot {d_{y}\left( {{3;1},4} \right)}} \right)}} +} \\{{{z_{4}\left( {x - x_{1}} \right)}\left( {x - x_{3}} \right)\left( {y - y_{1}} \right){\left( {y - y_{2}} \right)/\left( {{d_{x}\left( {{4;1},3} \right)} \cdot {d_{y}\left( {{4;1},2} \right)}} \right)}},}\end{matrix} & (12)\end{matrix}$

In a (2,3) situation, two of the four x-coordinate values are different(e.g., x1=x2≠x3=x4), and three of the y-coordinate values are differentfrom each other (e.g., y1≠y2=y3≠y4≠y3). In this (2,4) situation, theshape function is defined to be:

$\begin{matrix}\begin{matrix}{z = {f_{s}\left( {x,{y;2;3;{qu}}} \right)}} \\{= {{{z_{1}\left( {x - x_{3}} \right)}\left( {y - y_{2}} \right){\left( {y - y_{4}} \right)/\left( {{d_{x}\left( {1;3} \right)} \cdot {d_{y}\left( {{1;2},4} \right)}} \right)}} +}} \\{{{z_{2}\left( {x - x_{3}} \right)}\left( {y - y_{1}} \right){\left( {y - y_{4}} \right)/\left( {{d_{x}\left( {2;3} \right)} \cdot {d_{y}\left( {{2;3},4} \right)}} \right)}} +} \\{{{z_{3}\left( {x - x_{1}} \right)}\left( {y - y_{1}} \right){\left( {y - y_{4}} \right)/\left( {{d_{x}\left( {3;1} \right)} \cdot {d_{y}\left( {{3;1},4} \right)}} \right)}} +} \\{{{z_{4}\left( {x - x_{1}} \right)}\left( {y - y_{1}} \right){\left( {y - y_{2}} \right)/\left( {{d_{x}\left( {4;1} \right)} \cdot {d_{y}\left( {{4;1},2} \right)}} \right)}},}\end{matrix} & (13)\end{matrix}$

For the (3,2) situation, with three distinct x-coordinates values andtwo distinct y-coordinate values, the shape function z=f_(s)(x,y;3;2;qu)is defined analogous to the shape function z=f_(s)(x,y;2;3;qu) in Eq.(13).

In a (2,2) situation, two of the four x-coordinate values are different(e.g., x1=x2≠x3=x4), and two of the y-coordinate values are different(e.g., y4=y1≠y2=y3). In this (2,2) situation, the shape function isdefined to be:

$\begin{matrix}\begin{matrix}{z = {f_{s}\left( {x,{y;2;2;{qu}}} \right)}} \\{= {{{z_{1}\left( {x - x_{3}} \right)}{\left( {y - y_{2}} \right)/\left( {{d_{x}\left( {1;3} \right)} \cdot {d_{y}\left( {1;2} \right)}} \right)}} +}} \\{{{z_{2}\left( {x - x_{3}} \right)}{\left( {y - y_{1}} \right)/\left( {{d_{x}\left( {2;3} \right)} \cdot {d_{y}\left( {2;1} \right)}} \right)}} +} \\{{{z_{3}\left( {x - x_{1}} \right)}{\left( {y - y_{1}} \right)/\left( {{d_{x}\left( {3;1} \right)} \cdot {d_{y}\left( {3;1} \right)}} \right)}} +} \\{{{z_{4}\left( {x - x_{1}} \right)}{\left( {y - y_{2}} \right)/\left( {{d_{x}\left( {4;1} \right)} \cdot {d_{y}\left( {4;2} \right)}} \right)}},}\end{matrix} & (14)\end{matrix}$

More generally, the quadrilateral Q(1,2,3,4) can be replaced by anM-vertex polygon (M≧3) having non-zero included numerical area, and ashape function for this polygon is determined by analogy to thepreceding development. The simplest polygon here, having the lowestcorresponding polynomial degree in x and y, is a triangle (M=3). Theparticular shape function used will depend upon the configuration of thepolygon relative to the coordinate axes. For definiteness, it may beassumed here that the bone surface BS is divided by a grid ofquadrilaterals (or triangles) and that the coordinate values(x_(n),y_(n),z_(n)) (n=1, 2, 3, 4) of the vertices are known fromanalysis of the CT scan.

Where a sequence of triangles, rather than a sequence of quadrilaterals,is used to define a grid for the bone surface, as illustrated in FIG.12, three coordinate triples (x_(n),y_(n),z_(n)) (n=1, 2, 3) areprovided to define each such triangle. In a (3,3) situation, all threeof the x-coordinate values are different (x3≠x1≠x2≠x3), and all three ofthe y-coordinate values are different (y3≠y1≠y2≠y3). In this (3,3)situation, the shape function for a triangular grid is defined to be:

$\begin{matrix}\begin{matrix}{z = {f_{s}\left( {x,{y;3;3;{tr}}} \right)}} \\{= {{{z_{1}\left( {x - x_{2}} \right)}\left( {x - x_{3}} \right)\left( {y - y_{2}} \right){\left( {y - y_{3}} \right)/\left( {{d_{x}\left( {{1;2},3} \right)} \cdot {d_{y}\left( {{1;2},3} \right)}} \right)}} +}} \\{{{z_{2}\left( {x - x_{1}} \right)}\left( {x - x_{3}} \right)\left( {y - y_{1}} \right){\left( {y - y_{3}} \right)/\left( {{d_{x}\left( {{2;1},3} \right)} \cdot {d_{y}\left( {{2;1},3} \right)}} \right)}} +} \\{{z_{3}\left( {x - x_{1}} \right)}\left( {x - x_{2}} \right)\left( {y - y_{1}} \right){\left( {y - y_{2}} \right)/{\left( {{d_{x}\left( {{3;1},2} \right)} \cdot {d_{y}\left( {{3;1},2} \right)}} \right).}}}\end{matrix} & (15)\end{matrix}$

In a (2,3) situation, where only two x-coordinate values are different(e.g., x1=x2≠x3) and all three y-coordinate values are different, theshape function is defined to be:

$\begin{matrix}\begin{matrix}{z = {f_{s}\left( {x,{y;2;3;{tr}}} \right)}} \\{= {{{z_{1}\left( {x - x_{3}} \right)}\left( {y - y_{2}} \right){\left( {y - y_{3}} \right)/\left( {{d_{x}\left( {1;3} \right)} \cdot {d_{y}\left( {{1;2},3} \right)}} \right)}} +}} \\{{{z_{2}\left( {x - x_{3}} \right)}\left( {y - y_{1}} \right){\left( {y - y_{3}} \right)/\left( {{d_{x}\left( {2;3} \right)} \cdot {d_{y}\left( {{2;1},3} \right)}} \right)}} +} \\{{z_{3}\left( {x - x_{1}} \right)}\left( {y - y_{1}} \right){\left( {y - y_{2}} \right)/{\left( {{d_{x}\left( {3;1} \right)} \cdot {d_{y}\left( {{3;1},2} \right)}} \right).}}}\end{matrix} & (16)\end{matrix}$

For the (3,2) situation, with three distinct x-coordinates values andtwo distinct y-coordinate values, the shape function z=f_(s)(x,y;3;2;tr)is defined analogous to the shape function z=f_(s)(x,y;2;3;tr) in Eq.(16).

In a (2,2) situation, two of the three x-coordinate values are different(e.g., x1=x2≠x3), and two of the three y-coordinate values are different(e.g., y1≠y2=y3). In this (2,2) situation, the shape function is definedto be:

$\begin{matrix}\begin{matrix}{z = {f_{s}\left( {x,{y;2;2;{tr}}} \right)}} \\{= {{{z_{1}\left( {x - x_{3}} \right)}{\left( {y - y_{2}} \right)/\left( {{d_{x}\left( {1;3} \right)} \cdot {d_{y}\left( {1;2} \right)}} \right)}} +}} \\{{{z_{2}\left( {x - x_{3}} \right)}{\left( {y - y_{1}} \right)/\left( {{d_{x}\left( {2;3} \right)} \cdot {d_{y}\left( {2;1} \right)}} \right)}} +} \\{{z_{3}\left( {x - x_{1}} \right)}{\left( {y - y_{1}} \right)/{\left( {{d_{x}\left( {3;1} \right)} \cdot {d_{y}\left( {3;1} \right)}} \right).}}}\end{matrix} & (17)\end{matrix}$

Where a quadrilateral grid is used and, for a given quadrilateral,precisely M x-coordinate values are different and precisely Ny-coordinate values are different (2≦M≦4; 2≦N≦4), the shape function isa polynomial of degree M−1 in x and of degree N−1 in y. Utilizing thetheory of equations and roots of equations, one can show that the shapefunction defined in this manner for a quadrilateral, satisfyingf_(s)(x_(n),y_(n);M;N;qu)=z_(n) (n=1, 2, 3, 4) and having minimalpolynomial degree, is unique, although the polynomial itself may beexpressed in different, equivalent ways.

Where a triangular grid is used and, for a given triangular, precisely Mx-coordinate values are different and precisely N y-coordinate valuesare different (2≦M≦3; 2≦N≦3), the shape function is a polynomial ofdegree M−1 in x and of degree N−1 in y. Utilizing the theory ofequations and roots of equations, one can show that the shape functiondefined in this manner for a quadrilateral, satisfyingf_(s)(x_(n),y_(n);M;N;tr)=zn (n=1, 2, 3) and having minimal polynomialdegree, is unique, although the polynomial itself may be expressed indifferent, equivalent ways. The shape function polynomial for atriangular grid has smaller polynomial degree in x and in y (as small asdegree 1 in each of x and in y) than the corresponding shape functionpolynomial for a quadrilateral grid.

The shape function, f_(s)(x,y;M;N;tr) or f_(s)(x,y;M;N;qu), may be usedas is to describe a minimal polynomial surface for a particular polygonsatisfying f_(s)(x_(n),y_(n),M;N;tr or qu)=z_(n). If desired, the gridadopted may include a mixture of triangles and quadrilaterals, with eachsuch polygon having its own shape function. That is, if the gridincludes a total of K polygons (e.g., triangles and/or quadrilaterals),a total of K shape functions are defined, using the precedingmathematical construction.

(2) Bone surface normal mapping. The components of a vector n(x,y)normal to the bone surface defined by the shape function for aparticular quadrilateral are determined to be:n(x,y)={∂f _(s) /∂x,∂f _(s) /∂y,−1},  (18)

where the vector components can be, but need not be, normalized to unitlength, if desire. These normal vector components can be used todetermine the local surface normal n(x,y) for an implant device thatapproximates as closely as possible the bone surface BS imaged by the CTscan. Again, if the grid includes a total of K polygons (e.g., trianglesand/or quadrilaterals), a total of up to K shape functions are defined,using the preceding mathematical construction, and a surface normal at aselected location within each polygon is computed.

FIG. 13 illustrates a surface element SE, defined by three spaced apartlocations with Cartesian coordinates (x_(m),y_(m),z_(m)) (m=1, 2, 3),with each location having a surface normal of unit length n^(m) that isspecified, for example, by information from the CT image. With referenceto a spherical coordinate system (r,θ,φ) that is aligned as shown withthe Cartesian coordinate system, the vector components of a unit-lengthnormal at a given location are expressible as:n^=(cos φ sin θ, sin φ sin θ, cos θ),  (19)

A local surface element defined by the three locations(x_(m),y_(m),z_(m)) is approximated by a surface element of an ellipsoidthat is rotated by an angle y in the (x,y)-plane relative to thex-coordinate axis:{(x−x0)cos ψ+(y−y0)sin ψ}² /a ²+{−(x−x0)sin ψ+(y−y0)cos ψ}² /b ²+(z−z0)²/c ²−1,  (20)

where a, b and c are three positive numbers and x0, y0 and z0 are threecoordinate values, and ψ is a rotation angle, as yet unspecified.Locally, the ellipsoid surface can be re-expressed in functional formas:z(x,y)=z0±c{1−u ² −v ²}^(1/2),  (21)∂z/∂x=−(±)(c/a)u/{1−u ² −v ²}^(1/2),  (22)∂z/∂y=−(±)(c/b)v/{1−u ² −v ²}^(1/2),  (23)u={(x−x0)cos ψ+(y−y0)sin ψ}/a,  (24)v={−(x−x0)sin ψ+(y−y0)cos ψ}/b,  (25)

The expressions for ∂z/∂x and ∂z/∂y are strictly monotonic (increasingor decreasing) in each of the variables u and v and range from −∞ to +∞so that, for any pair of real numbers (w1,w2), unique values u and v canbe found for Eqs. (22) and (23) for which ∂z/∂x=w1 and ∂z/∂y=w2. Vectorcomponents for a unit-length normal vector for the surface z(x,y) areexpressible as:n^=(±(c/a)u,±(c/b)v,−{1−(c/a)² u ²−(c/b)² v ²}^(1/2)),  (26)

and unit-length surface normal vectors n^(m) are to be matched at threelocations, (x,y,z)=(x_(m),y_(m),z_(m)). Matching of the third of thesethree vector components is automatic (apart from the signum) for aunit-length vector. These vector components matching requirements areexpressed as:(c/a)u _(m) =c′{(x _(m) −x0)cos ψ+(y _(m) −y0)sin ψ}/a ²=cos φ_(m)·sinθ_(m),  (27A)(c/b)v _(m) =c′{−(x _(m) x0)sin ψ+(y _(m) −y0)cos Ψ}/b ²=sin φ_(m)·sinθ_(m),  (27B)

(m=1, 2, 3), where the right hand expressions are specified or measuredvalues. Equations (27A) and (27B) can also be rotated and therebyexpressed in the form:x _(m) −x0=(a ² /c)cos ψ cos φ_(m) sin θ_(m)−(b ² /c)sin ψ sin φ_(m) sinθ_(m),  (28A)y _(m) −y0=(a ² /c)sin ψ cos φ_(m) sin θ_(m)+(b ² /c)cos ψ sin φ_(m) sinθ_(m).  (28B)

Equations (27A) and (27B), or (28A) and (28B), are six equations in sixexplicit unknowns (x0, y0, ψ, a, b, c), and solutions can be found. Eachsurface element may have a different set of these unknowns, but twoadjacent surface elements with a common vertex will have the samesurface normal at that common vertex.

Once these six unknowns are determined, the ellipsoidal surface elementextending between the three locations or vertices (x_(m),y_(m),z_(m)) isdefined, with a surface normal that varies continuously from a surfacenormal at one of these vertices to a surface normal at another of thesevertices. These surface elements become part of a surface mosaic thatprovides a well-defined surface normal within the surface elementinterior. No matter which direction a surface element vertex isapproached, from within any surface element that has that vertex, thesurface normal vector will approach the same normal vector associatedwith that vertex. Although an ellipsoid, defined in Eq. (20) has beenused here, any other three-dimensional conic, such as a saddle surfacewith at least one + sign replaced by a − sign in Eq. (20), can be usedfor surface normal matching in appropriate circumstances.

(3) Bone surface-to-surface mapping. A surface-to-surface mapping is anextension of bone surface normal mapping, using a significantly largernumber of data points and surface normal vectors within selectedregions.

Construction of a mathematical model of a portion of a bone surface hasused polynomials in a Cartesian coordinate set (x,y,z). One could, aswell, use a multi-coordinate Fourier series, expressed in cylindricalcoordinates (r(θ,z),θ,z) or in another suitable coordinate set, for thelocation of selected points on a bone surface.

Any other suitable approach for point-to-point mapping and/or surfacenormal mapping can be used here to determine or estimate amathematically expressed surface for a selected portion of a bone.

Although the example herein has focused on TJA for a patient's knee, theprocedure is applicable to any other joint as well, such as a patient'ship, foot, toe, elbow, shoulder, wrist, finger or neck joint.

What is claimed is:
 1. A device configured to guide a transverseresection in a non-resected bone surface in a knee region of a leg boneduring an arthroplasty, the transverse resection creating a resectionplanar surface in the non-resected bone surface, the resection planarsurface including a resection position that allows the arthroplasty tobe completed such that an implant preoperatively selected forimplantation via the arthroplasty has an implanted position on the legbone, the implanted position being determined in a preoperative analysisof the leg bone and the implant prior to the manufacturing of the deviceand prior to the device being brought into contact with the non-resectedbone surface or employed in the arthroplasty, a first relationship ofthe resection position relative to the non-resected bone surface beingdetermined during the preoperative analysis when a representation of theimplant and an image of the leg bone are superimposed via a computer,the first relationship becoming part of a production file used in themanufacture of the device, the device comprising: a mating surfaceconfigured to engage the non-resected bone surface in a matching manneron account of a patient-specific nature of the mating surface, thematching manner registering a single relative position of the matingsurface relative to the non-resected bone surface, the patient specificnature of the mating surface having been generated in the device priorto the device being brought into contact with the bone surface oremployed in the arthroplasty; and a cutting instrument guide comprisinga guide position with a second relationship relative to the non-resectedbone surface when the non-resected bone surface is engaged by the matingsurface in the matching manner, the second relationship of the guideposition relative to the non-resected bone surface matching the firstrelationship of the resection position relative to the non-resected bonesurface with respect to position and orientation, the guide positionpreoperatively generated in the device prior to the device being broughtinto contact with the non-resected bone surface or employed in thearthroplasty.
 2. A device configured to guide a transverse resection ina non-resected bone surface in a knee region of a leg bone during anarthroplasty employing a knee implant, wherein a first relationshipbetween the transverse resection and the non-resected bone surface ispreoperatively planned by superimposing via a computer a representationof the knee implant and an image of the leg bone, the device comprising:a mating surface configured to engage the non-resected bone surface in amatching manner on account of a patient-specific nature of the matingsurface, the matching manner registering a single relative position ofthe mating surface relative to the non-resected bone surface, thepatient specific nature of the mating surface having been generated inthe device prior to the device being brought into contact with the bonesurface or employed in the arthroplasty; and a cutting instrument guidewith a second relationship relative to the non-resected bone surfacewhen the non-resected bone surface is engaged by the mating surface inthe matching manner, the second relationship of the cutting instrumentguide relative to the non-resected bone surface matching the firstrelationship of the transverse resection relative to the non-resectedbone surface with respect to position and orientation, the secondrelationship of the cutting instrument guide relative to thenon-resected bone surface preoperatively generated in the device priorto the device being brought into contact with the non-resected bonesurface or employed in the arthroplasty.
 3. The device as in any ofclaims 1 or 2, further comprising a jig body, and the mating surface isdefined in the jig body.
 4. The device of claim 3, wherein the cuttinginstrument guide further comprises a planar guide surface located on thejig body.
 5. The device as in any of claims 1 or 2, further comprising amember separate from and supported off of the jig body, the cuttinginstrument guide further comprising a planar guide surface located onthe member.
 6. The device of claim 5, wherein a portion of the membercontacts the jig body.
 7. The device of claim 6, wherein the cuttinginstrument guide further comprises another planar guide surface locatedon the jig body opposite the planar guide surface located on the member.8. The device as in any of claims 1 or 2, wherein the cutting instrumentguide includes a saw slot.
 9. The device as in any of claims 1 or 2,wherein the device is a femoral arthroplasty jig or a tibialarthroplasty jig.
 10. The device as in any of claims 1 or 2, wherein themating surface comprises a negative shape of the non-resected bonesurface.
 11. The device as in any of claims 1 or 2, wherein the matingsurface comprises surface profiles matching surface profiles of thenon-resected bone surface.
 12. The device as in any of claims 1 or 2,wherein the mating surface is a result of a CNC or SLA process.